Lottery Wheels

What is a Lottery Wheel?

A Lottery Wheel is a combinations generator. It generates a set of combinations of a group of numbers so that if certain conditions are met, the generated numbers will guarantee a win. Many players have a set of numbers to play such as birthdays and ages of their loved ones, but many times these set of numbers would be greater in number than those played by the lottery. For instance, a player may have ten favorites to play a 6 number lottery game. These numbers can be combined at random and played in two or more tickets, but a lottery wheel will combine the ten numbers systematically and generate two or more tickets that will guarantee a certain winning.

There is one thing that should be clear here. A lottery wheeel does not increase your chance of winning the lottery per se. The chance of winning is always increased by playing more than one ticket, that is, the more number of tickets you play, the better will be your chance of winning irrespective of whether you use a lottery wheel or not. However, if the winning numbers are in the group of your favorite numbers, at least one of the tickets generated by a lottery wheel will be a winner of either the jackpot or lesser prizes while randomly combining the numbers may not result in any winner.

Types of Lottery Wheels

Basicaly there are two types of lottery wheels called Full Wheels and Abbreviated wheels. Both of these types can be designed to incorporate some fixed numbers (also called key numbers), which will appear in all the generated numbers. So, we can classify lottery wheels as:
1. Full Wheels,
2. Full Wheeels with Fixed Numbers,
3. Abbreviated Wheels, and
4. Abbreviated Wheels with Fixed Numbers.

Full Lottey Wheel

A Full Wheel is simply a generator of all the possible combinations of a set of numbers into group of n numbers, where n is usually the game number (the number of numbers played in the game). For 6/49 lotto, n is 6. Since all the combinations of the set are played, a full wheel guarantees a winning equal to how many of the numbers in the set are winning numbers; if all the winning numbers are in the set then it guarantees a jackpot (and several lower prizes as well).

The drawback of these wheels is that the number of combinations generated are too many, thus too expensive. For example, all the possible 6-number combinations of a set of 10 numbers is 210; for a set of 20 numbers it is 38,760. Our combinations calculator and generator for n/N lottery games is actualy Full Wheel for n/N lottery games. And that is where the above figures are obtained from. Also, the combinations calculator and generator for n/N + 1/M lottery games is the Full Wheel for for n/N + 1/M lottery games.

Full Lottey Wheel with Fixed Numbers

This wheel is similar to the above except that some of the numbers are fixed. Fixing some numbers means that those numbers will appear in all the generated lottery tickets, and thus reducing the number of plays generated. The guaranteed wins in this case are equal to the sum of winning fixed numbers and the winning other selections.

The number of tickets generated will depend on how many numbers are fixed. For example, for 6-number combinations of a set of 10 numbers where three of them are fixed, there will be 35 combinations; for a set of 20 numbers with 3 fixed there will be only 680. Please see our Full Lottey Wheel with Fixed Numbers for n/N lottery games as well as Full Lottey Wheel with Fixed Numbers for n/N + 1/M lottery games.

Abbreviated Lottey Wheel

An Abbreviated Lottey Wheel generates a combination that is much less in number than that generated by full wheels to guarantee wins other than the jackpot. The design of an abbreviated wheel itself is not a simple matter; there is no formula for it and is mostly a result of iterations and trials and errors. In fact, in mathematics, it is called Covering Design and belongs to a branch of mathematics called Combinatorics.

There are hundreds of abbreviated wheels and each is represented mathematically by

C(v,k,t,m,=b)
In English, it reads as
"Covering of v sets of numbers combined into groups of k to guarantee at least a t if m numbers are correct, resulting in b plays."

Since there is no standard notation for the rest of us, we shall, in this website use the following notation to represent an abbreviated wheel:

"k-v, t if m in b", which means
"For a game of k numbers, v numbers are wheeled to guarantee t if m winners, in b combinations."

For example, a wheel represented by C(10,6,3,4,=5) or, by our notation as 6-10, 3 if 4 in 5 would be a wheel that generates 5 plays of a 6-number game from 10 numbers to guarantee at least a 3 if any 4 of the winning numbers are among the ten numbers. So, if use such a wheel on the ten numbers 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, the result would be:

Note that there is no unique abbreviated wheel for a given combination. For instance, you'll find wheels on the internet for a 6/49 lottery game to generate plays that guarantee a three by using all the 49 numbers. I have seen "6-49, 3 in 168", "6-49, 3 in 167", and "6-49, 3 in 163" (there is no 'if' since they cover all the numbers). The difference between these wheels is the number of plays to be generated, otherwise they all have the same purpose and result. In these situations the one that claims the minimum number of plays is the best since it is the least expensive. Whether it is a true claim or not is another question.

Abbreviated Lottey Wheel with Fixed Numbers

Just as it was done for Full Wheels, some numbers may be fixed in an abbreviated wheel as well. Although this sets more stringent conditions, it will result in either better guarateed wins, or smaller number of plays generated.